Theorems · Theorem · field theory
Real.exists_natCast_add_one_lt_pow_of_one_lt
∀ {a : ℝ}, 1 < a → ∃ m, ↑m + 1 < a ^ mExponentiation is eventually larger than linear growth.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- ne_of_gtproof · cited by 637
- one_divproof · cited by 624
- Int.cast_natCastproof · cited by 393
- mul_posproof · cited by 374
- Int.cast_oneproof · cited by 371
- div_posproof · cited by 337
Cited by1
Results whose statement or proof uses this declaration.